Every now and then - usually when talking with an older individual or someone from the United States Midwest or South - I hear the word "spell" used to mean a short period of time, such as: "Come sit down and rest a spell." I've also heard it used as a verb, like, "When Pete arrives he will spell Tito, who has been working since dawn."

What is the history and origins of this meaning and use of the word spell? And is it a colloquialism or can it be used in more formal settings?

spell seems folksy when used alone -- "Come over here and sit a spell." -- but much less so when used to cover a specific period of performing a specific task -- "When Bob got tired of conning the boat, I took a spell at the wheel."
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MalvolioJul 31 '11 at 19:07

To answer the latter part of your question "When Pete arrives he will spell Tito, who has been working since dawn."

Spell:
"work in place of (another)," Old English spelian "to take the place of," related to gespelia "substitute," of uncertain origin. Perhaps related to spilian "to play" (see spiel). Related: Spelled; spelling. The noun meaning "indefinite period of time" first recorded 1706.